Planar Filament with Directed Electron Beam

ABSTRACT

A planar filament 11f can include multiple materials to increase electron emission in desired directions and to suppress electron emission in undesired directions. The filament 11f can include a core-material CM between a top-material TM and a bottom-material BM. The top-material TM can have a lowest work function WFt; the bottom-material BM can have a highest work function WFb; and the core-material CM can have an intermediate work function WFc(WFt&lt;WFc&lt;WFb). A width Wt of the filament 11f at a top-side 31t can be greater than its width Wb at a bottom-side 31b (Wt&gt;Wb). This shape makes it easier to coat the edges 31e with the bottom-material BM, because the edges 31e tilt toward and partially face the sputter target. This shape also helps direct more electrons to a center of the target 14, and reduce electron emission in undesired directions.

CLAIM OF PRIORITY

This application claims priority to US Provisional Patent Application Number U.S. 63/147,969, filed on Feb. 10, 2021, which is incorporated herein by reference.

FIELD OF THE INVENTION

The present application is related generally to x-ray sources.

BACKGROUND

X-rays have many uses, including imaging, x-ray fluorescence analysis, x-ray diffraction analysis, and electrostatic dissipation. A large voltage between a cathode and an anode of the x-ray tube, and sometimes a heated filament, can cause electrons to emit from the cathode to the anode. The anode can include a target material. The target material can generate x-rays in response to impinging electrons from the cathode.

BRIEF DESCRIPTION OF THE DRAWINGS (DRAWINGS MIGHT NOT BE DRAWN TO SCALE)

FIG. 1a is a cross-sectional side-view of a transmission-target x-ray tube 10 a including a filament 11 _(f) configured to emit electrons in an electron beam 16 to a target 14. X-rays 17 can emit out of the x-ray tube 10 a through the target 14 and an adjacent x-ray window 13.

FIG. 1b is a cross-sectional side-view of a transmission-target x-ray tube 10 b, similar to x-ray tube 10 a. X-ray tube 10 b has a differently shaped anode 12 and electrically-insulative structure 15 than x-ray tube 10 a.

FIG. 2 is a cross-sectional side-view of a reflective-target, side-window x-ray tube 20 including a filament 11 _(f) configured to emit electrons in an electron beam 16 to a target 14. The target 14 can be configured to emit x-rays 17 through an interior of the x-ray tube 20, and out of the x-ray tube 20 through an x-ray window 13.

FIG. 3 is a top-view of a filament 11 _(f), with spiral and serpentine shapes.

FIG. 4 is a cross-sectional side-view of the filament 11 _(f) of FIG. 3, taken along line 4-4 in FIG. 3.

FIG. 5a is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a top-material TM at a top-side 31 _(t) and a bottom-material BM at a bottom-side 31 _(b).

FIG. 5b is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a top-material TM at a top-side 31 _(t), and with a bottom-material BM at a bottom-side 31 _(b) and at two edges 31 _(c).

FIG. 6a is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a top-material TM at a top-side 31 _(t), a bottom-material BM at a bottom-side 31 _(b), and a core-material CM between the top-material TM and the bottom-material BM.

FIG. 6b is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a top-material TM at a top-side 31 _(t), a bottom-material BM at a bottom-side 31 _(b) and at two edges 31 _(e), and a core-material CM between the top-material TM and the bottom-material BM.

FIG. 6c is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a top-material TM at a top-side 31 _(t), a bottom-material BM at a bottom-side 31 _(b) and at two edges 31 _(e), and a core-material CM between the top-material TM and the bottom-material BM.

FIG. 7 is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with a width W_(t) at the top-side 31 _(t) that is greater than a width W_(b) at the bottom-side 31 _(b).

FIG. 8a is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with combined features from FIGS. 5b and 7.

FIG. 8b is a cross-sectional side-view of a portion of a wire 31 of a filament 11 _(f), with combined features from FIGS. 6b and 7.

FIG. 9 is a top-view of a filament 11 _(f), with central regions 91 and 92.

FIG. 10 is a cross-sectional side-view of a filament 11 _(f), with wire width W_(t) greater than a gap width W_(g) between adjacent wires 31 (W_(t)>W_(g)).

Definitions. The following definitions, including plurals of the same, apply throughout this patent application.

As used herein, the term “elongated” means that wire length is substantially greater than wire width W_(t)(FIGS. 3-4) and wire thickness Th_(w)(FIG. 4). For example, wire length can be ≥5 times, ≥10 times, ≥100 times, or ≥1000 times larger than wire width W_(t), wire thickness Th_(w), or both.

As used herein, aligned with a plane (e.g. “aligned with a first plane” or “aligned with a second plane”) means exactly aligned; aligned within normal manufacturing tolerances; or almost exactly aligned, such that any deviation from exactly aligned would have negligible effect for ordinary use of the device.

As used herein, the term “parallel” means exactly parallel, or within 10° of exactly parallel. The term “parallel” can mean within 0.1°, within 1°, or within 5° of exactly parallel if explicitly so stated in the claims.

As used herein, the term “unparallel” means the lines or surfaces intersect at an angle greater than 10°.

As used herein, the term “perpendicular” means exactly perpendicular, or within 10° of exactly perpendicular. The term “perpendicular” can mean within 0.1°, within 1°, or within 5° of exactly perpendicular if explicitly so stated in the claims.

As used herein, the terms “on”, “located on”, “located at”, and “located over” mean located directly on or located over with some other solid material between. The terms “located directly on”, “adjoin”, “adjoins”, and “adjoining” mean direct and immediate contact.

As used herein, the term “μm” means micrometer(s).

Unless explicitly noted otherwise herein, all temperature-dependent values are such values at 25° C.

DETAILED DESCRIPTION

An x-ray tube can make x-rays by sending electrons, in an electron-beam, across a voltage differential, to a target.

A small electron spot and a controlled electron spot on the target are useful features of x-ray tubes. A small electron spot and a controlled electron spot can improve x-ray imaging and x-ray diffraction spectroscopy.

A lower filament temperature is another useful feature. Filaments last longer at lower temperatures. Thus, x-ray tube life can increase, resulting in improved reliability and less waste.

Reduced x-ray tube power consumption is another useful feature. Improved filament efficiency can reduce x-ray tube power consumption. Thus, any adverse impact on the environment, due to electrical power consumption, is reduced. Also, battery size of a portable x-ray source can be reduced, which can reduce operator fatigue and improve ergonomics of x-ray tube usage.

The present invention is directed to various x-ray tubes that satisfy the needs of

-   -   small electron spot,     -   controlled electron spot,     -   lower filament temperature,     -   reduced electrical power consumption,     -   green/environmentally-friendly, and     -   improved ergonomics.         Each x-ray tube may satisfy one, some, or all of these needs.

As illustrated in FIGS. 1a -2, x-ray tubes 10 a, 10 b, and 20 are shown with a cathode 11 and an anode 12 electrically-insulated from each other. An electrically-insulative structure 15 can separate and electrically-insulate the cathode 11 from the anode 12. The structure 15 (FIGS. 1a and 2) can be a cylinder and can have an evacuated interior between the cathode 11 and the anode 12. Example materials for the electrically-insulative structure 15 include glass, ceramic, or both.

The cathode 11 can include a filament 11 _(f), which can be heated by an electric current. This heat and/or a voltage differential between the cathode 11 and the anode 12 can cause the filament 11 _(f) to emit electrons in an electron beam 16 to a target 14. The target 14 can include a material for generation of x-rays 17 in response to impinging electrons from the filament 11 _(f).

In the transmission-target x-ray tubes 10 a and 10 b of FIGS. 1a and 1b , the target 14 can adjoin an x-ray window 13. The x-rays 17 can emit out of x-ray tubes 10 a and 10 b from the target 14 through the x-ray window 13.

In the reflective-target, side-window x-ray tube 20 of FIG. 2, the target 14 can be spaced apart from the x-ray window 13. The x-rays 17 can emit from the target 14 through an interior of the x-ray tube 20, and out of the x-ray tube 20 through an x-ray window 13.

Shape and materials of the filament 11 _(f) can be selected for a small electron spot on the target 14, a controlled electron spot on the target 14, a lower temperature of the filament 11 _(f), improved filament efficiency, or combinations thereof. As illustrated in FIGS. 3-4, the filament 11 _(f) can be an elongated wire 31. The filament 11 _(f) can be flat or planar. The wire 31 can include a spiral-shape, a serpentine-shape, or both.

The filament 11 _(f) can include (a) a top-side 31 _(t); (b) a bottom-side 31 _(b) opposite of the top-side 31 _(t); and (c) two edges 31 _(e), opposite of each other, extending between the top-side 31 _(t) and the bottom-side 31 _(b). The top-side 31 _(t) can face the target 14. The bottom-side 31 _(t) can face away from the target 14. The top-side 31 _(t) can be aligned with a first plane 41. The bottom-side 31 _(b) can be aligned with a second plane 42. The first plane 41 can be parallel to the second plane 42.

As illustrated in FIGS. 5a-6c and 8a-8b , the filament 11 _(f) can be made of multiple, different materials to increase electron emission in desired directions and to suppress electron emission in undesired directions. As illustrated in FIGS. 7-8 b, the filament 11 _(f) can have a shape to increase electron emission in desired directions and to suppress electron emission in undesired directions. These characteristics can provide a smaller and a more controlled electron spot on the x-ray tube target 14.

Also, because fewer electrons are emitted in undesirable directions, the filament 11 _(f) can be more efficient. Thus, temperature of the filament 11 _(f) can be reduced for a given x-ray flux. Reducing filament 11 _(f) temperature can increase filament 11 _(f) life, and thus also x-ray tube life. Increased x-ray tube life reduces energy and materials expended to manufacture x-ray tubes, thus improving the environment. Also, there is less need for waste disposal because of fewer scrapped x-ray tubes.

Reducing filament 11 _(f) temperature can also reduce power consumption, thus improving the environment. Reduced power consumption allows use of a smaller battery in a portable x-ray source, thus reducing x-ray tube weight. This reduces operator fatigue and improves ergonomics of use.

As illustrated in FIGS. 5a-b , the filament 11 _(f) can include a top-material TM at the top-side 31 _(t) and a bottom-material BM at the bottom-side 31 _(b). The top-material TM can adjoin the bottom-material BM. The bottom-material BM can suppress electron emission from the bottom-side 31 _(b). The top-material TM can increase electron emission from the top-side 31 _(t).

The top-material TM and the bottom-material BM can be different materials with respect to each other. A work function WF_(t) of the top-material TM can be lower than a work function WF_(b) of the bottom-material BM (WF_(t)<WF_(b)).

As illustrated in FIG. 5b , the bottom-material BM can also coat the two edges 31 _(e) of the filament 11 _(f). Thus, the bottom-material BM can also suppress electron emission from the two edges 31 _(e). The bottom-material BM can be a continuous layer, covering the bottom-side 31 _(b) and the two edges 31 _(e) with a thin film.

It is useful to suppress electron emission from the bottom-side 31 _(b), from the two edges 31 _(e), or both. An initial trajectory of these electrons is not towards the target 14. Many of these electrons can hit undesirable locations, such as the electrically-insulative structure 15. This can put an electrical charge on the electrically-insulative structure 15, which can deflect the electron beam or cause arcing failure of the tube. Thus, suppression of electron emission from the bottom-side 31 _(b) and from the two edges 31 _(e) improves x-ray tube reliability and life. This can improve efficiency of the worker, increasing output, and can reduce strain on the environment.

Without the invention, some of the electrons emitted in undesirable directions can change their trajectory and reach the target 14; but relatively few will hit a center of the target 14. Thus, they can cause an undesirably large or distorted spot. This can reduce accuracy and efficiency of x-ray imaging and x-ray diffraction spectroscopy. Therefore, suppressing emission of electrons from the bottom-side 31 _(b) and from the two edges 31 _(e) is desirable. One example of the invention suppresses this emission by use of the bottom-material BM.

The filament 11 _(f) of FIG. 5b is preferable over the filament 11 _(f) of FIG. 5a for suppressing electron emission in undesirable directions. The filament 11 _(f) of FIG. 5a , however, might be preferred for manufacturability.

The filament 11 _(f) of FIG. 5a can be made by sputter deposition of the bottom-material BM on a sheet of the top-material TM, or sputter deposition of the top-material TM on a sheet of the bottom-material BM. A laser can then ablate material of the sheet to form a shape of the filament 11 _(f).

The filament 11 _(f) of FIG. 5b can be made by cutting a sheet of the top-material TM to form a shape of the filament 11 _(f). The bottom-material BM can be sputter deposited at the bottom-side 31 _(b) and on the two edges 31 _(e). Oblique angle deposition from multiple angles may be needed to deposit the bottom-material BM on the two edges 31 _(e).

As illustrated in FIGS. 6a-6c , the filament 11 _(f) can include a core-material CM between the top-material TM and the bottom-material BM. As illustrated in FIGS. 6b-6c , the top-material TM and the bottom-material BM can encircle the core-material CM. The top-material TM and the bottom-material BM can enclose completely the core-material CM.

The top-material TM, the bottom-material BM, and the core-material CM can be different materials with respect to each other. The top-material TM can have a lowest work function WF_(t); the bottom-material BM can have a highest work function WF_(b); and the core-material CM can have an intermediate work function WF_(c)(WF_(t)<WF_(c)<WF_(b)). This arrangement of materials, with work function as noted, can increase electron emission from the top-side 31 _(t), which faces the target 14, and decrease electron emission from the bottom-side 31 _(b) (and also at the two edges 31 _(e) for filaments 11 _(f) of FIGS. 6b-6c and 8a-8b ). Thus, more electrons can be directed to a smaller spot on the target 14.

The filament 11 _(f) of FIG. 6a can be made by sputter deposition of (a) the bottom-material BM on one side of a sheet of the core-material CM, and (b) the top-material TM on an opposite side of a sheet of the core-material CM. These steps may be performed in either order. A laser can then ablate material of the sheet to form a shape of the filament 11 _(f). The laser can cut from the bottom-material BM side, from the top-material TM side, or both.

The filament 11 _(f) of FIG. 6b can be made by cutting a sheet (e.g. laser ablation) of the core-material CM to form a shape of the filament 11 _(f). The bottom-material BM can then be sputter deposited at the bottom-side 31 _(b) and on the two edges 31 _(e). Oblique angle deposition of the bottom-material BM from multiple angles may be needed to deposit the bottom-material BM on the two edges 31 _(e). The top-material TM can be sputter deposited at the top-side 31 _(t).

The filament 11 _(f) of FIG. 6c can be made by cutting a sheet (e.g. laser ablation) of the core-material CM to form a shape of the filament 11 _(f). The top-material TM can be sputter deposited at the top-side 31 _(t). Alternatively, the top-material TM can be sputter deposited at the top-side 31 _(t) prior to laser ablation, and the core-material CM and the top-material TM can be cut together. The bottom-material BM can then be sputter deposited at the bottom-side 31 _(b) and on the two edges 31 _(e). Oblique angle deposition of the bottom-material BM from multiple angles may be needed to deposit the bottom-material BM on the two edges 31 _(e).

The filaments 11 _(f) of FIGS. 6a-6c are preferable over the filaments 11 _(f) of FIGS. 5a and 5b if a top-material TM, with low work function WF_(t), lacks other desirable characteristics. For example, hafnium (preferred as a top-material TM) has a low work function (desirable), but is also expensive (undesirable). Cost of the filament 11 _(f) can be reduced by adding a less expensive core material CM (e.g. tungsten), thus reducing the mass and cost of hafnium in the filament 11 _(f).

Example top-materials TM include barium, cesium, hafnium, thorium, or combinations thereof. Example core-materials CM include tungsten, molybdenum, titanium, or combinations thereof. Example bottom-materials BM include cobalt, copper, gold, iridium, iron, nickel, osmium, rhenium, rhodium, ruthenium, or combinations thereof.

Tungsten, molybdenum, and titanium could also be top-materials, especially in the example of FIGS. 5a-b , with no separate core-material CM. Thus, example materials for the top-material TM include barium, cesium, hafnium, thorium, tungsten, molybdenum, titanium, or combinations thereof.

The top-material TM, the core-material CM, and the bottom-material BM can include a high percent of a single element, such as for example ≥50, ≥75, ≥90, or ≥98 weight percent of one of the elements noted in the preceding paragraphs.

Factors to consider in selection of these materials include cost, work function (WF_(t)<WF_(c)<WF_(b)), melting temperature (high enough to not melt during operation), low vapor pressure (avoid degrading the vacuum inside the tube), and durability of the coating (avoid flaking). Another factor to consider is reactivity. The filament 11 _(f) can fail if it reacts with gases and changes its chemical composition. For the bottom-material BM, the ability to braze to filament supports is another factor to consider.

The bottom-material BM can have a thickness Th_(b) sufficiently large to aid in soldering to a support, and to suppress electron emission, but not too thick in order to avoid flaking. Example thicknesses Th_(b) of the bottom-material BM in the final filament 11 _(f) include 0.2 μm≤Th_(b), 1 μm≤Th_(b), or 2.5 μm≤Th_(b); and Th_(b)≤2.5 μm, Th_(b)≤5 μm, Th_(b)≤15 μm.

The top-material TM can have a thicknesses Th_(t) sufficiently large to increase electron emission, but not too thick to distract from valuable attributes of the core material CM, bottom-material BM, or both. Example thicknesses Th_(t) of the top-material TM in the final filament 11 _(f) include 0.2 μm≤Th_(t), 1 μm≤Th_(t), or 2.5 μm≤Th_(t); and Th_(t)≤5 μm, Th_(t)≤10 μm, Th_(t)≤20 μm.

As illustrated in FIG. 7, a width W_(t) of the wire 31 at the top-side 31 _(t) can be greater than a width W_(b) of the wire 31 at the bottom-side 31 _(b) (W_(t)>W_(b)). This shape can help direct more electrons to a center of the target 14, and reduce electron emission in undesired directions. This shape also can make it easier to coat the edges 31 _(e) with the bottom-material BM, because the edges 31 _(e) tilt toward and partially face the sputter target. Example relationships between W_(t) and W_(b) include 1.05≤W_(t)/W_(b), 1.2≤W_(t)/W_(b), 1.4≤W_(t)/W_(b), or 1.5≤W_(t)/W_(b); and W_(t)/W_(b)≤1.5, W_(t)/W_(b)≤1.75, W_(t)/W_(b)≤2, W_(t)/W_(b)≤5, or W_(t)/W_(b)≤25. Both widths W_(t) and W_(b) can be measured perpendicular to a length of the wire 31.

An internal angle A_(i) of the filament 11 _(f), between the top-side 31 _(t) and each of the edges 31 _(e), can also be selected to achieve the benefits mentioned in the prior paragraph. For example, A_(i)≤85°, A_(i)≤80°, or A_(i)≤70°; and A_(i)≥20°, A_(i)≥45°, A_(i)≥60°, or A_(i)≥70°. The filament 11 _(f) can have such angle A_(i) along a large portion of its length, such as for example along at least 50%, 80%, 95%, or 100% of a length of the filament 11 _(f).

Example cross-sectional shapes of the filament 11 _(f) include trapezoid and triangle shapes. The top-side 31 _(t) can be parallel to the bottom-side 31 _(b). The two edges 31 _(e) can be unparallel with respect to each other. The two edges 31 _(e) can extend linearly between the top-side 31 _(t) and the bottom-side 31 _(b).

The above shapes can be formed by patterning the bottom-side 31 _(b), then isotropic etching. The above shapes can be formed by cutting the filament 11 _(f) with a laser. More laser time can be used at a center of a gap between adjacent wires 31. Laser time can taper down moving closer toward a center of the wire 31. The amount of taper can be adjusted between gradual and sharp, to change the angle A_(i) and W_(t)/W_(b).

A relationship, between a width W_(t) of the wire 31 at the top-side 31 _(t) and a thickness Th_(w) of the wire 31, can be selected for improved overall strength of the wire 31 and increased emission of electrons from the top-side 31 _(t). For example, 1.2≤W_(t)/Th_(w), 1.4≤W_(t)/Th_(w), or 1.9≤W_(t)/Th_(w); and W_(t)/Th_(w)≤1.9, W_(t)/Th_(w)≤3, W_(t)/Th_(w)≤5. The width W_(t) can be selected by the pattern of the desired shape. The thickness Th_(w) can be selected by choice of initial material thickness, plus coatings, if any. Th_(w) is a thickness of the wire 31 between the top-side 31 _(t) and the bottom-side 31 _(b), measured perpendicular to a plane of the top-side 31 _(t).

The top-material TM can cover all of the top-side 31 _(t). But, it can be useful to cover a smaller percentage of the surface. Illustrated in FIG. 9 are central regions 91 and 92. By coating the top-side 31 _(t) with the top-material TM within one of these central regions 91 or 92, the electron beam can be narrowed, with a larger portion of the electron beam coming from a center of the filament 11 _(f). This can form a very small spot on the target 14, which is valuable for some applications.

By covering only the central region 91 or 92 of the filament 11 _(f) with the top-material TM, each end of the wire 31 can be free of the top-material TM. To do this, layer(s) of material for the filament 11 _(f) can be patterned to block ends of the wire 31, and leave a central region 91 or 92 open while depositing the top-material TM. Thus, the top-material TM can be deposited only in the central region 91 or 92. This patterning and deposition can be done before or after cutting to form the wires 31. Thus for example, the top-material TM can cover ≥5%, ≥25%, or ≥50%; and ≤50%, ≤80%, or ≤90% of the top-side 31 _(t), which coverage can be or include the central region 91 or 92.

It is preferable for the bottom-material BM to cover all or nearly all of the bottom-side 31 _(b) and of the two edges 31 _(e), such as for example ≥75%, ≥90%, or ≥95% of the bottom-side 31 _(b) and the two edges 31 _(e).

A width W_(t) of the wire 31 and a width W_(g) of a gap between adjacent wires 31 is illustrated in FIGS. 3-4 and 10. Both the width W_(t) of the wire 31 and the width W_(g) of a gap are measured at the top-side 31 _(t) of the wire 31 and perpendicular to a length of the wire 31 (i.e. perpendicular to the length at the point of measurement).

In FIGS. 3-4, the width W_(g) of the gap is larger than the width W_(t) of the wire 31 (W_(g)>W_(t)), except for a small central region of the wire 31. In FIG. 10 the width W_(t) of the wire 31 is greater than the width W_(g) of the gap (W_(t)>W_(g)). The smaller gap in FIG. 10 (W_(t)>W_(g)) increases radiative cross heating between adjacent parts of the wire 31. This allows a smaller electrical current to produce the same temperature, thus saving electrical power.

Duty cycle DC is used to quantify the relationship between W_(t) and W_(g) (DC=W_(t)/W_(g)). Example duty cycles DC, for balancing heating efficiency with robustness of the filament 11 _(f), include 1.05≤DC, 1.15≤DC, or 1.25≤DC; and DC≤1.25, DC≤1.5, DC≤2. The duty cycles DC can apply across the entire filament 11 _(f). Alternatively, the duty cycle DC values just noted can be an average across a limited portion of the filament 11 _(f), such as for example ≥50%, ≥75%, or ≥90%; and ≤99% of a central region of the filament 11 _(f). 

What is claimed is:
 1. An x-ray tube comprising: a cathode and an anode electrically insulated from one another, the cathode including a filament configured to emit electrons to a target at the anode, the target configured to emit x-rays in response to impinging electrons from the filament; the filament being an elongated wire in a planar shape with a top-side facing the target, a bottom-side opposite of the top-side, and two edges, opposite of each other, extending between the top-side and the bottom-side, the top-side aligned with a first plane, and the bottom-side aligned with a second plane, the first plane being parallel to the second plane; W_(t)>W_(b), where W_(t) is a width of the wire measured at the top-side and perpendicular to a length of the wire and W_(b) is a width of the wire measured at the bottom-side and perpendicular to the length of the wire; the filament has a top-material at the top-side and a bottom-material at the bottom-side and at the two edges; and the top-material is different from the bottom-material, and WF_(t)<WF_(b), where WF_(t) is a work function of the top-material and WF_(b) is a work function of the bottom-material.
 2. The x-ray tube of claim 1, wherein the top-material includes hafnium and the bottom-material includes nickel.
 3. The x-ray tube of claim 1, further comprising: a core-material between the top-material and the bottom-material; the top-material, the bottom-material, and the core-material are different materials with respect to each other; and WF_(t)<WF_(c)<WF_(b), where WF_(c) is a work function of the core-material.
 4. The x-ray tube of claim 3, wherein: a material composition of the top-material includes ≥75 weight percent hafnium; a material composition of the bottom-material includes ≥75 weight percent nickel; and a material composition of the core-material includes ≥75 weight percent tungsten.
 5. The x-ray tube of claim 1, wherein a cross section of the filament has a trapezoid shape, the top-side is parallel to the bottom-side, and the two edges are unparallel with respect to each other.
 6. The x-ray tube of claim 1, wherein 1.05≤W_(t)/W_(b)≤2.
 7. The x-ray tube of claim 1, wherein 1.2≤W_(t)/Th_(w)≤3, where Th_(w) is a wire thickness between the top-side and the bottom-side, measured perpendicular to a plane of the top-side.
 8. An x-ray tube comprising: a cathode and an anode electrically insulated from one another, the cathode including a filament configured to emit electrons to a target at the anode, the target configured to emit x-rays in response to impinging electrons from the filament; the filament being an elongated wire with a top-side facing the target, a bottom-side opposite of the top-side, and two edges, opposite of each other, extending between the top-side and the bottom-side; A_(i)≤80°, where A_(i) is an internal angle of the filament between the top-side and each of the edges; the filament has a top-material at the top-side, a bottom-material at the bottom-side and at the two edges, and a core-material between the top-material and the bottom-material, the top-material, the bottom-material, and the core-material being different materials with respect to each other; and WF_(t)<WF_(c)<WF_(b), where WF_(t) is a work function of the top-material, WF_(c) is a work function of the core-material, and WF_(b) is a work function of the bottom-material.
 9. The x-ray tube of claim 8, wherein the top-material includes hafnium, barium, cesium, thorium, or combinations thereof; the bottom-material includes iridium, nickel, gold, copper, or combinations thereof; and the core-material includes tungsten, molybdenum, or both.
 10. The x-ray tube of claim 8, wherein 1 μm≤Th_(b)≤5 μm, where Th_(b) is a thickness of the bottom-material; and 1 μm≤Th_(t)≤10 μm, where Th_(t) is a thickness of the top-material.
 11. The x-ray tube of claim 8, wherein the top-material covers ≥90% of the top-side, and the bottom-material covers ≥90% of the bottom-side and ≥90% of the two edges.
 12. The x-ray tube of claim 8, wherein the top-material covers ≥5% and ≤80% of the top-side, the top-material covers a central region of a length of the wire, and each end of the wire is free of the top-material.
 13. The x-ray tube of claim 8, wherein 60°≤A_(i).
 14. An x-ray tube comprising: a cathode and an anode electrically insulated from one another, the cathode including a filament configured to emit electrons to a target at the anode, the target configured to emit x-rays in response to impinging electrons from the filament; the filament is an elongated wire with a top-side facing the target, a bottom-side opposite of the top-side, and two edges, opposite of each other, extending between the top-side and the bottom-side; and A_(i)≤80°, where A_(i) is an internal angle of the filament between the top-side and the edge.
 15. The x-ray tube of claim 14, wherein: the elongated wire includes a spiral-shape, a serpentine-shape, or both; and an average duty cycle (DC) is ≥1.05 and ≤1.5 across ≥50% of a central region of the filament, where DC=W_(t)/W_(g), W_(t) is a width of the wire measured at the top-side and perpendicular to a length of the wire, and W_(g) is a width of a gap between adjacent wires measured at the top-side and perpendicular to the length of the wire.
 16. The x-ray tube of claim 14, wherein 60°≤A_(i).
 17. The x-ray tube of claim 14, wherein A_(i)≤80° along at least 80% of a length of the filament.
 18. The x-ray tube of claim 14, wherein a cross section of the filament has a trapezoid shape, the top-side is parallel to the bottom-side, and a width of the top-side is greater than a width of the bottom-side.
 19. The x-ray tube of claim 14, wherein the two edges are unparallel with respect to each other.
 20. The x-ray tube of claim 14, wherein the two edges extend linearly between the top-side and the bottom-side. 